﻿the 
  Ions 
  of 
  Gases. 
  349 
  

  

  Per 
  unit 
  area 
  it 
  is 
  proportional 
  to 
  

  

  R-2rf{<^(R) 
  + 
  >/r(R)}/dm, 
  

   and 
  the 
  chano-e 
  of 
  this 
  for 
  change 
  dK 
  is 
  

  

  But 
  the 
  associated 
  stress 
  F' 
  is 
  proportional 
  to 
  c?R/R, 
  so 
  in 
  

   this 
  case 
  the 
  force 
  restoring 
  unitbrmitj 
  when 
  the 
  system 
  of 
  

   ion 
  and 
  molecules 
  is 
  strained 
  is 
  proportional 
  to 
  

  

  F'R^[R-2c^{<^(R) 
  + 
  f 
  (R)}/^R]/^R 
  

  

  and 
  also 
  to 
  FyT, 
  so 
  that 
  T~^ 
  is 
  proportional 
  to 
  

  

  R^[R-2J{(^(R) 
  + 
  ^|r(R)}/^R]/iR. 
  

  

  Now 
  we 
  know 
  that 
  for 
  two 
  electrons 
  the 
  potential 
  varies 
  as 
  

   1/R, 
  for 
  an 
  electron 
  and 
  an 
  electric 
  doublet 
  as 
  1/R^, 
  and 
  for 
  

   two 
  doublets 
  as 
  1/R^. 
  In 
  the 
  nctual 
  case 
  at 
  distance 
  R 
  the 
  

   form 
  of 
  (^(R) 
  + 
  '\/r(R) 
  is 
  almost 
  that 
  of 
  1/R^, 
  as 
  will 
  appear 
  

   in 
  Table 
  II. 
  : 
  hence 
  in 
  the 
  product 
  NT 
  we 
  get 
  a 
  result 
  pro- 
  

   portional 
  to 
  R^/R^, 
  that 
  is, 
  a 
  constant. 
  Thus 
  in 
  a 
  gas 
  this 
  

   factor 
  of 
  6 
  is 
  independent 
  of 
  the 
  density, 
  just 
  as 
  the 
  ordinary 
  

   Tiscosity 
  of 
  a 
  gas 
  is. 
  In 
  the 
  previous 
  reasoning 
  we 
  have 
  

   considered 
  only 
  the 
  molecules 
  which 
  are 
  immediate 
  neigh- 
  

   bours 
  of 
  an 
  ion. 
  Similar 
  reasoning 
  applies 
  to 
  the 
  next 
  more 
  

   remote 
  lot 
  of 
  neighbours 
  and 
  so 
  on. 
  It 
  is 
  important 
  to 
  notice 
  

   that 
  the 
  argument 
  by 
  which 
  this 
  factor 
  of 
  6 
  was 
  proved 
  

   independent 
  of 
  density 
  makes 
  it 
  also 
  independent 
  of 
  the 
  

   nature 
  of 
  the 
  gas 
  ; 
  it 
  is 
  a 
  universal 
  constant. 
  To 
  the 
  above 
  

   reasoning 
  we 
  must 
  add 
  the 
  statement 
  that 
  T 
  is 
  proportional 
  

   to 
  F, 
  so 
  that 
  NT 
  and 
  therefore 
  6 
  is 
  proportional 
  to 
  F^ 
  which 
  

   varies 
  from 
  one 
  gas 
  to 
  another. 
  In 
  applying 
  these 
  new 
  

   viscosities 
  f 
  and 
  6 
  in 
  the 
  study 
  of 
  the 
  motion 
  of 
  ions 
  through 
  

   gases 
  we 
  treat 
  6 
  as 
  acting 
  just 
  like 
  F, 
  while 
  as 
  regards 
  f 
  we 
  

   consider 
  it 
  to 
  act 
  over 
  area 
  q~^^ 
  with 
  a 
  relative 
  motion 
  

   U1 
  — 
  U2 
  between 
  two 
  neighbour 
  ions 
  at 
  distance 
  9~^'^ 
  apart, 
  Ui 
  

   being 
  the 
  velocity 
  of 
  the 
  positive 
  ion 
  and 
  «2 
  of 
  ftie 
  negative, 
  

   so 
  that 
  the 
  resistance 
  experienced 
  by 
  an 
  electron 
  is 
  

  

  W 
  \ 
  -2,3/ 
  -13 
  

  

  For 
  the 
  motion 
  of 
  the 
  ions 
  in 
  a 
  field 
  of 
  intensity 
  d'E/dx 
  we 
  

   have 
  the 
  equations 
  

  

  ^^=?(«i-".)r^-'+(^+F)ui] 
  

  

  -«^=-r(«>-».)9-'"+(^+FK 
  

  

  y 
  • 
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